Generalised geometry for string corrections

TL;DR

This paper develops a formalism within generalised geometry to incorporate string corrections, extending the tangent bundle and defining a universal action, with applications to heterotic and type II string theories.

Contribution

It introduces a new formalism for string corrections in generalised geometry, including bundle extensions and a universal action based on a generalized Lichnerowitz--Bismut theorem.

Findings

String corrections linear in α' are incorporated for heterotic strings.

No such corrections are found for type II theories.

The formalism requires specific choices of generalized connections.

Abstract

We present a general formalism for incorporating the string corrections in generalised geometry, which necessitates the extension of the generalised tangent bundle. Not only are such extensions obstructed, string symmetries and the existence of a well-defined effective action require a precise choice of the (generalised) connection. The action takes a universal form given by a generalised Lichnerowitz--Bismut theorem. As examples of this construction we discuss the corrections linear in $\alpha'$ in heterotic strings and the absence of such corrections for type II theories.